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What is the midpoint of a line segment with the endpoints [tex]\((-6, -3)\)[/tex] and [tex]\((9, -7)\)[/tex]?

A. [tex]\((1, -4.5)\)[/tex]
B. [tex]\((-5, 1.5)\)[/tex]
C. [tex]\((1.5, -5)\)[/tex]
D. [tex]\((-4.5, 1)\)[/tex]



Answer :

GinnyAnswer
To determine the midpoint of a line segment with given endpoints [tex]\((-6, -3)\)[/tex] and [tex]\( (9, -7)\)[/tex], we use the midpoint formula. The midpoint of a line segment with endpoints [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by:

[tex]\[ \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \][/tex]

In this case, the coordinates of the endpoints are:

- [tex]\(x_1 = -6\)[/tex]
- [tex]\(y_1 = -3\)[/tex]
- [tex]\(x_2 = 9\)[/tex]
- [tex]\(y_2 = -7\)[/tex]

Now, we substitute these values into the midpoint formula:

[tex]\[ \text{Midpoint}_x = \frac{-6 + 9}{2} \][/tex]
[tex]\[ \text{Midpoint}_x = \frac{3}{2} \][/tex]
[tex]\[ \text{Midpoint}_x = 1.5 \][/tex]

Next, we find the midpoint's y-coordinate:

[tex]\[ \text{Midpoint}_y = \frac{-3 + (-7)}{2} \][/tex]
[tex]\[ \text{Midpoint}_y = \frac{-10}{2} \][/tex]
[tex]\[ \text{Midpoint}_y = -5 \][/tex]

Hence, the coordinates of the midpoint are:

[tex]\[ (1.5, -5) \][/tex]

So, the correct answer is:

C. [tex]\((1.5, -5)\)[/tex]

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